Russia was referring to the Syrian Democratic Forces (SDF), an alliance of Kurdish and Arab militias fighting with the US-led coalition, which Moscow said had diverted from the battle to take Raqqa to Deir al-Zor, where Russian special forces are helping the Syrian army push out ISIS terrorists.
The Russian Defence Ministry said the SDF had taken up positions on the eastern banks of the Euphrates with US special forces, and had twice opened fire with mortars and artillery on Syrian troops who were working alongside Russian special forces.
"A representative of the US military command in Al Udeid (the US operations centre in Qatar) was told in no uncertain terms that any attempts to open fire from areas where SDF fighters are located would be quickly shut down," Major-General Igor Konashenkov said in a statement.
"Fire points in those areas will be immediately suppressed with all military means."
In Deir al-Zor province of eastern Syria, ISIS is battling two separate offensives, launched by the SDF on one side and the Syrian army and its allies on the other.
Syrian troops also crossed to the eastern side of the river on Monday. The SDF's advances have been on the eastern bank of the river.
The convergence of the two rival offensives has increased tensions in Deir al-Zor. The US-backed militia said on Saturday they had come under attack from Russian jets and Syrian government forces, something Moscow denied.
The SDF warned on Monday against any further Syrian army advances on the eastern riverbank.
On Tuesday Russia's Defence Ministry said the waters of the Euphrates had risen as soon as the Syrian army began crossing it, suggesting this could only have happened if upstream dams held by the U.S.-backed opposition had been opened.
Konashenkov, in his Thursday statement, questioned the nature of SDF's relationship with ISIS. Russian drones did not detect any clashes between the two groups when SDF fighters approached Deir al-Zor, he said.